Archimedes in the Middle Ages, Vol. 4: A supplement on the - download pdf or read online

By Marshall Clagett

ISBN-10: 087169137X

ISBN-13: 9780871691378

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Additional info for Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part i

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Mn mg. inf. scr. m. 2 Nota quod linea ucx est maior quam linea qmn, similiter linea eh que comparatur seu correspondet linee ucx est maior quam linea eh que correspondet linee qmn, sicut enim crescit linea ucx super lineam qmn similiter crescit linea eh correspondens linee ucx super lineam eh correspondentem linee qmn [Lemma] 4 supra Inveniatur scr. m. 2 per 14 secundi 12-13 de Eadem . . duplicata mg. scr. m. 2 per 18 sexti 15 10 corr. 1The knowledge of conic sections revealed in these translations is found in Archimedes’ On the Equilibrium o f Planes, On the Quadrature of the Parabola, On Conoids and Spheroids and On Floating Bodies, as well as in Eutocius’ Com­ mentary on the Sphere and the Cylinder o f Archimedes and his Commen­ tary on the Equilibrium o f Planes o f Archimedes.

Secetque ipsam alia superficies erecta super trigonum ABC, non per verticem, secundum sectionem que sit EFG, cuius supremus punctus sit F, et sit linea EG equidistans alicui dyametro basis pyramidis, cuius medius punctus sit H; et ducatur linea FH a supremo puncto sectionis ad medium sue basis. Et quia linea EG est linea recta que est equidistans dyametro basis pyramidis, et punctum F signatum est in superficie conica, ubi in supremo, superficies EFG secat conicam super­ ficiem. Si itaque sectio EFG sit trigonum rectilineum, patet quod (correxi ex quoniam) due linee longitudinis pyramidis, que sunt EF et GF, concurrunt in puncto F preter verticem pyramidis, quod est impossible et contra 91am huius.

Tractatus . . concurrentibus] addidi Proemium [Proemium] addidi 9 de sagitta mg. scr. m. 1 sagitta et axis eius 55 56 ARCHIMEDES IN THE MIDDLE AGES 5 io 15 5 io 15 20 Esto piramis abg super circulum b g , et sint duo puncta d, e in superficie eius non in opposicione capitis que coniungat lineade recta [Fig. 1]. Dico lineam de ire intus in piramidem. Quoniam protraham a puncto a per d et e lineas rectas in superficie piramidis usque ad eius basim sintque adb, aeg et quia super circumferenciam circuli bg signata sunt duo puncta b , g , linea recta coniungens ea secat circulum.

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Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part i by Marshall Clagett


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